(32m^6/4n^4)^2

Jasonbradley

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Jun 16, 2024

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Simplifying (32m^6/4n^4)^2

This problem involves simplifying an expression with exponents and fractions. Here's how to break it down:

Understanding the Rules

• Exponents: When raising a power to another power, we multiply the exponents. For example, (x^m)^n = x^(m*n)
• Fractions: When raising a fraction to a power, we apply the power to both the numerator and denominator. For example, (a/b)^n = a^n/b^n

Applying the Rules

1. Simplify the inside of the parentheses:

   • 32/4 = 8
   • m^6 / n^4 remains as is.
   • Now we have (8m^6/n^4)^2

2. Apply the exponent to both the numerator and denominator:

   • (8m^6)^2 / (n^4)^2

3. Apply the exponent rule for powers of powers:

   • 8^2 * m^(62) / n^(42)

4. Simplify:

   • 64m^12 / n^8

Final Answer

The simplified expression is 64m^12 / n^8.